Question: Simplify; express your answer in exponential form. Assume $x\neq 0, p\neq 0$. $\dfrac{{(x^{5})^{4}}}{{(x^{-3}p^{5})^{-5}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${x^{5}}$ to the exponent ${4}$ . Now ${5 \times 4 = 20}$ , so ${(x^{5})^{4} = x^{20}}$ In the denominator, we can use the distributive property of exponents. ${(x^{-3}p^{5})^{-5} = (x^{-3})^{-5}(p^{5})^{-5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(x^{5})^{4}}}{{(x^{-3}p^{5})^{-5}}} = \dfrac{{x^{20}}}{{x^{15}p^{-25}}}$ Break up the equation by variable and simplify. $\dfrac{{x^{20}}}{{x^{15}p^{-25}}} = \dfrac{{x^{20}}}{{x^{15}}} \cdot \dfrac{{1}}{{p^{-25}}} = x^{{20} - {15}} \cdot p^{- {(-25)}} = x^{5}p^{25}$.